Question

How do you identify the important parts of `g(x)= x^2-4x+4` to graph it?

Answer 1

Intercept: 4
Minimum value: `(2,0)`

Explanation:

From the equation, any number behind `x` is the intercept. So from this equation you know that the intercept is `4`.

Next, complete the square so that the equation is in the form of `a(x+h)^2+k`. This will give you the minimum points of the graph.

If you don't know how to complete a square, it's like this:

1. Divide the coefficient of `x` by `2`
2. Take the square out of the `x`, so you will get `(x-2)^2`
3. Then square the `2` inside the bracket, which gets you `(x-2)^2-4+4`
4. Finally simplify the equation. `(x-2)^2`

Since there is no number after the brackets, the minimum value of `y` is `0`.

Minimum points= `(2,0)`
(Always switch the negative signs into positive and vice versa for the completed square!)

graph{x^2-4x+4 [-7.19, 8.614, -0.26, 7.64]}